Does martial arts help improve other skills in athletics?
Yes and I had children, tweens, and teens that parents would sometimes enroll in my school for that reason. Lack of balance and coordination was another big reason why some would enroll their children as well. I even had a rich adult come in one day and enroll in my school to improve his golf game. He was spending several hundred dollars a month on lessons with a couple of golf pros and it was not working out like he wanted. Someone suggested he try martial arts. After eight months or so he quit the lessons with the golf pros and told me I did more to improve his golf game than all the money and time he had spent on those lessons with those pros over the past year and gave me a nice bonus.
Most likely yes!
Yes by far!. Dallas Cowboys in the late 70's or early 80's actually hired a martial arts instructor and taught martial arts to the team. And they found that they performed very well doing such. And if memory serves correct a few other NFL teams did the same thing. It is even known that children with ADD AD/HD that have gone to a "karate school" and were able to control the children better. And the grades improve as well as discipline and attitude. Another is if you ever noticed how high school and college students who are multi-sport athletes who basically all year play sports, have usually better GPA than just the academic students plus being healthy. Also it teaches how to balance a schedule. So yes it helps in all aspects.